Medical image processing method and apparatus

ABSTRACT

A medical imaging data processing apparatus comprises processing circuitry configured to obtain a first imaging data set comprising a set of pixels or voxels, the first imaging data set being reconstructed from first measurement data representative of measurements of a measurement volume obtained by relative rotation of a medical scanner and the measurement volume by a first range of angles during a first scanning time period; obtain a second imaging data set comprising a set of pixels or voxels, the second imaging data set being reconstructed from second measurement data representative of measurements of the measurement volume obtained by relative rotation of the medical scanner and the measurement volume by a second range of angles during a second scanning time period, wherein the second scanning time period overlaps the first scanning time period such that some angles are included in both the first range of angles and the second range of angles; transform the first imaging data set to obtain a first transformed data set that is representative of the first measurement data as a function of at least one of angle or time; transform the second imaging data set to obtain a second transformed data set that is representative of the second measurement data as a function of at least one of angle or time; and determine at least one angle of the first range of angles and/or second range of angles based on differences between the first transformed data set and second transformed data set.

FIELD

Embodiments described herein relate generally to a method of, andapparatus for, obtaining at least one rotation angle from medicalimaging data, for example obtaining at least one CT gantry rotationangle from two or more medical imaging data sets.

BACKGROUND

Image quality in CT scans of the heart may be affected by heart motion.Motion of the heart within the duration of a cardiac CT scan capture mayresult in the presence of motion artifacts in images derived from thecardiac CT scan.

Some methods for motion compensation in CT are known in which motion(for example, cardiac motion) is estimated based on three reconstructionvolumes at close time points within a single rotation of a scanner. Forexample, in a scanner having a rotation time of 275 ms, threereconstruction volumes may be obtained at around 70 ms apart and motionmay be estimated based on those reconstruction volumes. It is known toperform motion compensated reconstruction, in which a new reconstructionvolume with reduced artifacts is obtained using the estimated motion.

In some circumstances, such motion compensation methods may be tightlyintegrated into a CT scanner system or other scanner apparatus and mayuse information obtained directly from the scanner itself but that isnot available from standard DICOM tags. Such information may be notavailable from, or stored with, reconstructed imaging data. Therefore,it can sometimes be difficult to apply motion compensation methods tostored imaging data or data processed remotely from the scanner systemitself, or data processed at a later time after completion of the scanmeasurements.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments are now described, by way of non-limiting example, and areillustrated in the following figures, in which:

FIG. 1 is a schematic illustration of an apparatus according to anembodiment;

FIG. 2 is a flow chart illustrating in overview a method of anembodiment;

FIG. 3 is a schematic illustration of a difference of Fouriertransformations of two input images;

FIGS. 4a and 4b each show a schematic illustration of ranges of gantryangles for a pair of datasets, and a determined approximate principalangle.

DETAILED DESCRIPTION

Certain embodiments provide a medical imaging data processing apparatuscomprising processing circuitry configured to obtain a first imagingdata set comprising a set of pixels or voxels, the first imaging dataset being reconstructed from first measurement data representative ofmeasurements of a measurement volume obtained by relative rotation of amedical scanner and the measurement volume by a first range of anglesduring a first scanning time period; obtain a second imaging data setcomprising a set of pixels or voxels, the second imaging data set beingreconstructed from second measurement data representative ofmeasurements of the measurement volume obtained by relative rotation ofthe medical scanner and the measurement volume by a second range ofangles during a second scanning time period, wherein the second scanningtime period overlaps the first scanning time period such that someangles are included in both the first range of angles and the secondrange of angles; transform the first imaging data set to obtain a firsttransformed data set that is representative of the first measurementdata as a function of at least one of angle or time; transform thesecond imaging data set to obtain a second transformed data set that isrepresentative of the second measurement data as a function of at leastone of angle or time; and determine at least one angle of the firstrange of angles and/or second range of angles based on differencesbetween the first transformed data set and second transformed data set.

Certain embodiments provide a medical imaging data processing methodcomprising: obtaining a first imaging data set comprising a set ofpixels or voxels, the first imaging data set being reconstructed fromfirst measurement data representative of measurements of a measurementvolume obtained by relative rotation of a medical scanner and themeasurement volume by a first range of angles during a first scanningtime period; obtaining a second imaging data set comprising a set ofpixels or voxels, the second imaging data set being reconstructed fromsecond measurement data representative of measurements of themeasurement volume obtained by relative rotation of the medical scannerand the measurement volume by a second range of angles during a secondscanning time period, wherein the second scanning time period overlapsthe first scanning time period such that some angles are included inboth the first range of angles and the second range of angles;transforming the first imaging data set to obtain a first transformeddata set that is representative of the first measurement data as afunction of at least one of angle or time; transforming the secondimaging data set to obtain a second transformed data set that isrepresentative of the second measurement data as a function of at leastone of angle or time; and determining at least one angle of the firstrange of angles and/or second range of angles based on differencesbetween the first transformed data set and second transformed data set.

An imaging data processing apparatus 10 according to an embodiment isillustrated schematically in FIG. 1. The imaging data processingapparatus 10 comprises a computing apparatus 12, for example, a personalcomputer (PC) or workstation, which is connected to a CT scanner 14, oneor more display screens 16 and an input device or devices 18, such as acomputer keyboard, mouse or trackball.

Although in the present embodiment the computing apparatus 12 isconnected to the CT scanner 14, in other embodiments the computingapparatus 12 is a workstation that is not connected to a CT scanner 14.The computing apparatus 12 may be a workstation that is configured toprocess stored CT data, for example CT data that has been stored in aPicture Archiving and Communication System (PACS).

The CT scanner 14 may be any CT scanner that is configured to obtaintwo-dimensional or three-dimensional CT scan data that is representativeof a region of a patient or other subject. In alternative embodiments,the CT scanner 14 may be replaced or supplemented by a scanner in anyother imaging modality, for example a cone-beam CT scanner, MRI(magnetic resonance imaging) scanner, X-ray scanner, PET (positronemission tomography) scanner, SPECT (single photon emission computedtomography) scanner, or ultrasound scanner.

In the present embodiment, the region for which scan data is obtained isan anatomical region of a patient, comprising the heart. In otherembodiments, the region may be any appropriate region. For example, theregion may comprise any appropriate vessel (for example, the coronaryarteries) or organ (for example, the lung or liver). The region of thepatient that is scanned may be referred to as a measurement volume.

The CT scanner 14 is configured to scan the region of the patient usingan X-ray source and receiver mounted on a gantry. The gantry performs afull 360° rotation around the patient in a rotation time, which in thepresent embodiment is 275 ms. In some circumstances, a full rotation maybe completed within a single heartbeat of the patient.

During each rotation, the receiver generates a plurality of subsets ofCT scan data, each subset corresponding to a different time during therotation and therefore to a different angle of rotation. Each subset ofdata may be representative of an attenuation of X-rays passing from thesource through the patient to the receiver at a respective angle ofrotation. Each subset of data may comprise, for example, voltage data.

In the present embodiment, each full rotation around the patientprovides CT scan data that is representative of an axial slice of theregion of the patient. In other embodiments, the CT scanner 14 may be aspiral CT scanner providing spiral CT scan data that is capable of beingprocessed to obtain axial slice data.

In the description below, the term scan data set (for example, CT scandata set) is used to refer to raw (unreconstructed) data. CT scan datamay be representative of measurements obtained by the scanner during aCT scan, for example voltage data that is obtained by the receiver ateach of a plurality of angles of rotation. A CT scan data set maycomprise data that is representative of one or more axial slices. Insome circumstances, a CT scan data set may be referred to as a sinogram.

In the present embodiment, CT scanner 14 comprises scannerreconstruction circuitry 15 that is configured to reconstruct CT scandata to obtain imaging data. It is a principle of CT scanning that CTscan data for a plurality of angles of rotation may be reconstructed toobtain imaging data comprising a plurality of pixels or voxels, eachpixel or voxel being representative of a corresponding location in themeasurement volume. Each pixel or voxel may comprise or be associatedwith a respective intensity value that is, for example, representativeof attenuation of X-rays at the corresponding location in space, forexample the corresponding location in the measurement volume.

In the description below, the term imaging data set is used to refer toreconstructed data. An imaging data set may be used to obtain an imageof the measurement volume, for example for display.

In the present embodiment, the CT scanner 14 reconstructs the CT data toobtain imaging data by using filtered back-projection. In otherembodiments, any suitable reconstruction method may be used.

Taking the example of a single axial slice, CT scan data for that axialslice is obtained during 360° of rotation of the gantry. An imaging dataset that is a full reconstruction of the axial slice may be obtained byusing CT scan data obtained during 180° of rotation of the gantry. It istherefore possible to obtain several full reconstructions of the axialslice, with each full reconstruction using CT scan data from a different180° (or more) of gantry rotation angles.

In the present embodiment, the scanner reconstruction circuitry 15 isconfigured to reconstruct, for each axial slice, several imaging datasets, each imaging data set being reconstructed from CT scan data for adifferent range of gantry rotation angles.

Each imaging data set is reconstructed from CT scan data for a different180° of gantry rotation angles. Therefore, the ranges of gantry rotationangles used for different reconstructions overlap. For example, for agiven slice, the scanner reconstruction circuitry 15 may reconstruct afirst imaging data set using CT scan data for a first range of gantryangles from 0° to 180° and a second imaging data set using CT scan datafor a second range of gantry angles from 90° to 270°. In reconstructingeach imaging data set from CT scan data, the scanner reconstructioncircuitry 15 makes use of information regarding the gantry rotationangles.

If no motion were to occur in the measurement volume during rotation, itmay be expected that each of the imaging data sets may be substantiallyidentical. However, the presence of motion may cause differences betweenthe imaging data sets reconstructed from different angular ranges (andtherefore representative of different times). For example, a shapeand/or position of the heart may change between the scanning time periodfor the first imaging data set and the scanning time period for thesecond imaging data set.

Imaging data sets that are output by the CT scanner 14 do not generallyinclude data relating to the range of gantry angles of the CT scan datafrom which they were reconstructed. Therefore, in some circumstances, itmay not be possible for a user receiving an imaging data set (forexample, a user receiving the imaging data set as a DICOM file) todetermine the range of gantry angles from which that imaging data setwas reconstructed. For example, a user consulting a DICOM file for animaging data set may not be able to determine from the DICOM filewhether that imaging data set has been reconstructed from a range ofgantry rotation angles from 0° to 180° or a range of gantry rotationangles from 90° to 270°.

A plurality of imaging data sets output by the CT scanner 14 are storedin memory 20 and subsequently provided to computing apparatus 12. Eachof the imaging data sets comprises a respective full reconstruction ofone or more axial slices. Each of the imaging data sets wasreconstructed using CT scan data for a different range of gantryrotation angles. The imaging data sets are stored without anyinformation regarding the gantry rotation angles of the CT scan datafrom which each imaging data set is reconstructed.

In an alternative embodiment, imaging data sets are supplied from aremote data store (not shown) which may form part of a PACS. The memory20 or remote data store may comprise any suitable form of memorystorage. The imaging data sets are provided from the remote data storewithout any information regarding the gantry rotation angles of the CTscan data from which each imaging data set is reconstructed.

Computing apparatus 12 provides a processing resource for automaticallyor semi-automatically processing imaging data sets, and comprises acentral processing unit (CPU) 22. In the present embodiment, thecomputing apparatus 12 includes transformation circuitry 24 and analysiscircuitry 26.

In the present embodiment, the transformation circuitry 24 and analysiscircuitry 26 are each implemented in computing apparatus 12 by means ofa computer program having computer-readable instructions that areexecutable to perform the method of the embodiment. For example, thetransformation circuitry 24 and analysis circuitry 26 may each beimplemented as a respective computer program or algorithm that isexecutable by the computing apparatus 12, for example by the CPU 22.However, in other embodiments, the various units may be implemented asone or more ASICs (application specific integrated circuits) or FPGAs(field programmable gate arrays).

The computing apparatus 12 also includes a hard drive and othercomponents of a PC including RAM, ROM, a data bus, an operating systemincluding various device drivers, and hardware devices including agraphics card. Such components are not shown in FIG. 1 for clarity.

The system of FIG. 1 is configured to perform the method of anembodiment as described below with reference to FIG. 2, in which imagingdata sets are processed to obtain information about the gantry rotationangles at which that CT data from which they are reconstructed wasacquired. Such angular information may be subsequently used, forexample, in methods of motion estimation or motion compensation.

At stage 30 of the process of FIG. 2, the transformation circuitry 24receives a first imaging data set from the CT scanner 14 or from a datastore. The transformation circuitry 24 does not receive any informationabout the range of gantry rotation angles of the CT scan data from whichthe first imaging data set was reconstructed.

In the present embodiment, the first imaging data set comprisestwo-dimensional imaging data that is representative of an axial slice ofa patient. Each voxel of the first imaging data set may be considered tocorrespond to a respective pixel of a two-dimensional image A of theaxial slice. In other embodiments, the first imaging data set comprisesthree-dimensional imaging data, for example 3D image data that may beprojected to form a two-dimensional image A. The first imaging data setmay be representative of a plurality of axial slices.

At stage 32 of the process of FIG. 2, the transformation circuitry 24receives a second imaging data set from the CT scanner 14 or data store.The transformation circuitry 24 does not receive any information aboutthe range of gantry rotation angles of the CT scan data from which thesecond imaging data set was reconstructed.

In the present embodiment, the second imaging data set comprisestwo-dimensional imaging data that is representative of the same axialslice of the patient as the first imaging data set. Each voxel of thesecond imaging data set may be considered to correspond to a respectivepixel of a two-dimensional image B of the axial slice. In otherembodiments, the second imaging data set comprises three-dimensionalimaging data that is representative of the same three-dimensional regionas the first imaging data set. The second imaging data set may berepresentative of a plurality of axial slices.

The second imaging data set is representative of the same anatomicalregion of the same patient as the first imaging data set, but isreconstructed from imaging data acquired at different times. The firstimaging data set is reconstructed from measurements acquired during afirst scanning time period, during which the gantry rotated through afirst range of gantry rotation angles. The second imaging data set isreconstructed from measurements acquired during a second scanning timeperiod, during which the gantry rotated through a second range of gantryrotation angles. The second scanning time period overlaps with the firstscanning time period. Therefore, the second range of gantry rotationangles overlaps with the first range of gantry rotation angles.Measurements for gantry angles obtained in the overlap between the firstscanning time period and second scanning time period are used in thereconstruction of both the first imaging data set and the second imagingdata set.

Angles that are part of both the first range of gantry rotation anglesand the second range of gantry rotation angles may be referred to asoverlapping angles. Angles that are part of the first range of gantryrotation angles and not part of the second range of gantry rotationangles, or angles that are part of the second range of gantry rotationangles and not part of the first range of gantry rotation angles, may bereferred to as non-overlapping angles.

Since the computing apparatus 12 does not at this stage have access toinformation (for example, DICOM information) about the gantry rotationangles used in reconstructing each of the first imaging data set andsecond imaging data set, the computing apparatus 12 processes the firstimaging data set and second imaging data set to obtain an estimate of atleast one of the gantry rotation angles.

At stage 34, the transformation circuitry 24 performs a two-dimensionalfast Fourier transform (2D FFT) of the first imaging data set to obtaina discrete Fourier transform 36 (DFT A) of the first imaging data set.In other embodiments, any method of implementing a discrete Fouriertransform may be used, which may or may not be a fast Fourier transform.In some embodiments, direct calculation of the discrete Fouriertransform is used.

In other embodiments, any suitable transformation may be used. Severalrelated specializations and generalizations of the Fourier transformexist. In some embodiments, one of those specializations orgeneralizations may be used in place of the Fourier transformation. Insome embodiments, the transformation comprises, for example, anumber-theoretic transform (NTT), a discrete weighted transform (DWT),or a Chirp Z-transform.

The transformation circuitry 24 passes DFT A to the analysis circuitry26.

The transformed first imaging data set, DFT A, comprises a plurality ofelements in a Fourier transform space, each with an associatedmagnitude. The elements may be described as pixels. An intensity of eachpixel may be representative of a magnitude of a Fourier transformcoefficient represented by that pixel. The transformed data set may berepresentative of the CT scan data as a function of at least one ofangle or time, for example angle between the scanner and the measurementvolume. Some of the low frequency information in the originalmeasurement may be lost during reconstruction (for example, there may beredundancy in the raw data, which is averaged out when creating thereconstructed image). However, most of the detail of the CT scan datamay be present and represented in the transformed data set.

As a result of the central slice theorem (also known as theprojection-slice theorem or the Fourier slice theorem), if a radial lineis drawn through the origin of the transformed first imaging data set atan angle ϕ, pixels on that radial line may be considered to correspondto CT scan data obtained at gantry angle ϕ or at gantry angle ϕ+180°.The Fourier transformed first data set, DFT A, has a fixed origin.

Although in the description below we have referred to pixels on a linethrough the transformed imaging data set at angle ϕ as corresponding toCT scan data obtained at gantry angle ϕ, in some embodiments the termgantry angle is used to refer to the angle of a line from the source(for example, X-ray tube) to the centre of a detector (for example,X-ray receiver). The corresponding line of sinogram data is orthogonalto the line from the source to the centre of the detector. So a linethrough the transformed imaging data set at an angle ϕ may correspond toa gantry angle of ϕ+90° or ϕ−90°.

At stage 38, the transformation circuitry 24 performs a two-dimensionalfast Fourier transform of the second imaging data set to obtain adiscrete Fourier transform 40 (DFT B) of the first imaging data set. Inother embodiments, any suitable transformation may be used to transformboth the first imaging data set and the second imaging data set. Thetransformation circuitry 24 passes DFT B to the analysis circuitry 26.

At stage 42, the analysis circuitry 26 subtracts DFT A and DFT B toobtain a difference data set. In other embodiments, any method ofobtaining a difference between DFT A and DFT B may be used. Differencesbetween DFT A and DFT B may be expressed in any suitable format. Anysuitable method of analysing difference data may be used.

In the present embodiment, the difference data set comprises a pluralityof pixels corresponding to the plurality of pixels of each of DFT A andDFT B. An intensity of each of the plurality of pixels in the differencedata set is representative of a magnitude of the difference between theintensity for that pixel in DFT A and the intensity of that pixel in DFTB. If the intensity of a pixel is substantially the same in DFT A as inDFT B, the intensity of that pixel in the difference data set is low. Ifthe intensity of a pixel is different in DFT A from in DFT B, theintensity of that pixel in the difference data set is higher.

FIG. 3 shows an image of a difference data set obtained by subtracting aDFT of a first imaging data set and a DFT of a second imaging data set,where the first imaging data set and second imaging data set are sets oftwo-dimensional imaging data (for example, axial slice data) that areobtained for the same anatomical region using CT data from different,overlapping ranges of gantry angles.

Processes below that are described as being performed on a differenceimage (for example, the difference image of FIG. 3) may in practice beperformed on the difference data set, for example without an image ofthe difference data set being rendered. For example, where drawing aline through the difference image is described, the analysis circuitry26 may in practice select pixels of the difference data set that, ifdisplayed, would fall on a line across the difference image. Similarly,processes performed on the difference data set may be described in termsas if they were performed on an image (for example, drawing a line orcircle on the difference data set or selecting a region of thedifference data set).

Pixels of the difference data set that appear as bright pixels in theimage of FIG. 3 are pixels where there is a difference between theintensity of that pixel in DFT A and the intensity of that pixel in DFTB. Pixels of the difference data set that appear dark in FIG. 3 arepixels where there is little or no difference between the intensity ofthat pixel in DFT A and the intensity of that pixel in DFT B.

Consider a radial line through the difference data set at an angle ϕ₁corresponding to a gantry angle ϕ₁ from which CT scan data was includedin both the reconstruction of the first imaging data set and thereconstruction of the second imaging data set (i.e. an angle ϕ₁ thatlies within the overlap of the first range of gantry rotation angles andthe second range of gantry rotation angles).

Since the same CT scan data was used for angle ϕ₁ in the first imagingdata set as was used in the second imaging data set, pixels on a radialline through DFT A at angle ϕ₁ may be expected to be substantially thesame as pixels on a radial line through DFT B at angle ϕ₁. Therefore,pixels on a radial line through the difference data set at angle ϕ₁ maybe expected to be dark (indicating low or no difference between thetransformed data sets).

On the other hand, consider a radial line through the difference dataset at an angle ϕ₂ corresponding to a gantry angle ϕ₂ from which CT scandata was included in the reconstruction of the first imaging data setand not the second imaging data set (or included in the reconstructionof the second imaging data set and not the first data set).

As an example, the first imaging data set may include data from gantryangle ϕ=10° and the second imaging data set may not include data fromgantry angle ϕ=10° but may include data from gantry angle ϕ=190°. Inthis example, the data obtained at gantry angle ϕ=190° is obtained at alater time than the data obtained at gantry angle ϕ=10°. It is possiblethat there may have been motion in the anatomical region between theacquisition of data at ϕ=10° and the acquisition of data at ϕ=190°.

Acquiring data from opposite directions (for example from ϕ=190° insteadof ϕ=10°) may give different results due to beam hardening and/or due toany effects other than simple attenuation. For example, differentresults may arise due to different scatter, which may often be seen inmetal artifacts. Data acquired from opposite directions may also bedifferent because they are different samples, and any noise captured maybe different.

Pixels on a radial line through DFT A at angle ϕ₂ may be expected to bedifferent from pixels on a radial line through DFT B at angle ϕ₂. Pixelson a radial line through the difference data set at angle ϕ₂ may beexpected to be bright.

In some embodiments, motion occurs between the acquisition of data atopposite angles (for example, between the acquisition of data at ϕ=10°and the acquisition of data at ϕ=190°). In other embodiments, no motionoccurs, or only minor motion occurs. Differences due to noise may besufficient to observe a bright line in the difference data set even ifthere is no motion, or only minor motion. A small amount of motion maycause a large difference in the phase of the Fourier transforms.

In practice, the CT scan data may be processed before or duringreconstruction. For example, filtering or noise reduction may be appliedto the CT scan data. It may therefore be the case that even for angles ϕthat were used in the reconstruction of both imaging data sets, theremay be some difference in the transformed imaging data sets. However,such differences may be expected to be less than the differences betweenangles ϕ for which different CT scan data was used in the reconstructionof each imaging data set. Differences due to filtering or noisereduction may result in small bright features on the difference data set(for example, bright lines or individual bright pixels) whereas a rangeof non-overlapping angles may appear in the difference data set as alarge bright region.

In the image of FIG. 3, two bright fan-shaped regions 50, 52 arevisible. The bright fan-shaped regions 50, 52 correspond tonon-overlapping angles (angles for which data used in the reconstructionof one of the first imaging data set and second imaging data set is notused in the reconstruction of the other of the first imaging data setand second imaging data set).

In FIG. 3, there are also some lines of brightness 54 that are not partof the bright fan-shaped regions 50, 52. The lines of brightness may beconsidered to be orthogonal to a range of angles of the fan-shapedregions 50, 52. These lines of brightness may be due to processing thatis applied to the CT scan data before reconstruction, or in thereconstruction of the imaging data sets, for example filtering or noisereduction. Some noise in the image of FIG. 3 may also be due toprocessing before or after reconstruction.

At stage 44 of the process of FIG. 2, the analysis circuitry 26 analysesthe difference data set to estimate at least one gantry rotation angle.In the present embodiment, the analysis circuitry 26 analyses thedifference data set to estimate a midpoint of a range of non-overlappingangles (angles for which data used in the reconstruction of one of thefirst imaging data set and second imaging data set was not used in thereconstruction of the other of the first imaging data set and secondimaging data set). For example, in the example of FIG. 3, the analysiscircuitry may estimate a midpoint of a range of non-overlapping anglescorresponding to bright region 50 and/or a midpoint of a range ofnon-overlapping angles corresponding to bright region 52.

In the present embodiment, the analysis circuitry 26 obtains themagnitude of each pixel of the difference data set, and uses themagnitude of the pixels to obtain the midpoint of the non-overlappingregions. Since each imaging data set is reconstructed from a respective180° of rotation, non-overlapping region 50 is offset fromnon-overlapping region 52 by 180°. A single radial line on FIG. 3 can beused to obtain the midpoint of both non-overlapping regions 50, 52.

In some embodiments, the analysis circuitry 26 applies a logarithmoperator to the difference data set, for example to make the differencedata set more suitable for display. The logarithm operator replaces eachpixel value x with log (1+|x|). The replacement of each pixel value xwith log (1+|x|) compresses the dynamic range of the difference data setimage so that it may be easier to see patterns in it.

The applying of the logarithm operator may decrease the brightness of acentral region of the difference data set relative to the rest of thedifference data set. If the brightness of the central region isdecreased, a viewer of an image rendered from the difference data setmay be able to see features of the difference data set more easily, forexample to see the bright fan-shaped regions 50, 52.

In other embodiments, no logarithm operator may be used. In someembodiments, a different type of transform may be applied to thedifference data set instead of or in addition to the logarithm operator.The difference data set may be processed using any method for processingFourier transform images for visual presentation.

In the present embodiment, the analysis circuitry 26 defines a set ofradial lines, each of which passes through the centre of the differencedata set at a respective angle ϕ. For each of the radial lines, theanalysis circuitry determines a sum of squares of the magnitude of thepixels of the difference data set along that radial line. The analysiscircuitry 26 selects the one of the radial lines for which the sum ofsquares is largest (which may be considered to be the radial line havingthe brightest pixels). The analysis circuitry uses the selected radialline to obtain an estimate of the midpoint of each of thenon-overlapping ranges of angles.

An example of a selected radial line 60 is drawn on FIG. 3. The selectedradial line 60 is an estimate of a midpoint of the bright fan regions50, 52.

In the example of FIG. 3, the imaging data sets from which thedifference data set is formed are from a 4D sequence, and differ byabout 20° of gantry rotation. The range of angles corresponding tonon-overlapping times is brighter than other angles, with theapproximate midpoint of the non-overlapping range of angles marked withline 60.

In the present embodiment, the midpoint is obtained automatically. Inother embodiments, the difference data set may be displayed to a user,and the user may estimate the midpoint. In some circumstances, thedifference data set image may be indistinct, and the angles may bedetermined by a user rather than automatically. In some circumstances,the determination of the angles may be crowdsourced as an alternative todetermining the angles algorithmically.

Although in the present embodiment a midpoint of the non-overlappingangles is determined, in other embodiments any suitable gantry angle maybe estimated: for example, a midpoint of a non-overlapping region, amidpoint of an overlapping region, or a boundary between an overlappingregion and a non-overlapping region.

In other embodiments, any suitable method may be used to estimate one ormore gantry rotation angles. The analysis circuitry 26 may use anysuitable method to analyse differences between two 2D Fouriertransformations of each slice to determine a range of radial anglescorresponding to sinogram data that is not shared by the imaging datasets. The central slice theorem implies that radial lines at theseangles are overall brighter than lines at angles corresponding to shareddata.

The sum of squares method described above may be particularly useful inthe case of imaging data sets for which the ranges of angles have aconsiderable overlap. In the example shown in FIG. 3, the first imagingdata set and second imaging data set are reconstructed from ranges ofangles that are offset by 20°. In some circumstances (for example, insome circumstances in which the offset is larger, for example 90°), thesum of squares method may perform more poorly.

In some embodiments, the analysis circuitry 26 fits a two-dimensionalfunction to the difference data set. In some embodiments, the 2Dfunction is based on a dipole radiation pattern. In some embodiments,the 2D function is a 2D Gaussian. The analysis circuitry 26 determinesan angle of a principal axis of the fitted 2D function. The angle of theprincipal axis is used as an estimate of a midpoint of a non-overlappingrange of angles.

In some embodiments, the analysis circuitry 26 determines a profilealong a circular trajectory around the centre of the difference dataset. The analysis circuitry 26 may smooth the resulting profile, forexample to reduce effects of noise. The analysis circuitry 26 determinesat least one peak in the determined profile. The analysis circuitry usesa position of a peak as an estimate of the midpoint of thenon-overlapping range of angles. In some such embodiments, the analysiscircuitry 26 may also use model fitting.

In some embodiments, the analysis circuitry 26 uses a Fouriertransformation method inspired by the DART registration algorithm (see,for example, Maas, Frederick, Renshaw, Decoupled automated rotationaland translational registration for functional MRI time series data: theDART registration algorithm, Magnetic Resonance in Medicine, 1997) toobtain an estimated angle. A profile is taken on a circular trajectoryas described above. A spectral decomposition of this profile (forexample, a spectral decomposition obtained by performing aone-dimensional Fourier transform) may be expected to have a dominantcomponent corresponding to a sine wave with a 180° period. The phase ofthat sine wave may be related to the midpoint of the non-overlappingangle. If the phase of the sine wave is θ°, the midpoint may be at(θ+90°)/2.

In some embodiments, the analysis circuitry 26 estimates a line ofreflective symmetry in the difference data set. The line of reflectivesymmetry may be a line of approximate reflective symmetry. Thedifference data set may not have exact reflective symmetry (although itmay have exact 180° rotational symmetry). The analysis circuitry usesthe line of reflective symmetry as an estimate of the midpoint of anon-overlapping region.

In other embodiments, any suitable method may be used to determine anyappropriate angle of the first range of gantry rotation angles used inthe reconstruction of the first imaging data set, or any appropriateangle of the second range of gantry rotation angles used in thereconstruction of the second imaging data set. For example, the analysiscircuitry 26 may estimate an angle in an overlapping region, an angle ina non-overlapping region, or an angle on a boundary between anoverlapping region and a non-overlapping region.

In the embodiment described in relation to FIG. 3, the first imagingdata set and second imaging data set are representative of a singleaxial slice. In other embodiments, the first imaging data set and secondimaging data set are representative of a plurality of axial slices.

In one embodiment, a first imaging data set comprises a reconstructionof several axial slices, each reconstructed from data for a first rangeof angles (for example, 0° to 180°).

A second imaging data set comprises a reconstruction of the same axialslices, each reconstructed from data for a second range of angles (forexample, 90° to 270°).

A two-dimensional Fourier transform may be applied to each slice and adifference data set may be obtained by taking the difference of thetransformed first imaging data set and the transformed second imagingdata set. Data from a plurality of slices may be used in estimating anangle, for example for estimating a midpoint of a non-overlapping rangeof angles.

In some embodiments, each multiple-slice volume is treated as a singledata set, but the DFT is computed separately on several slices of eachvolume. Once the DFTs are obtained, they are combined and thecombination of the DFTs is used to determine a single range of angles.

Helical data sets may be treated differently, because each slice of ahelical data set is acquired over a different range of angles. Allslices of the helical data set may be considered to be related, buttheir angles may depend on z position instead of all being the same.

In some embodiments, multiple slices may be combined beforetransformation. However, in some circumstances, doing the transformationand difference slice-by-slice may give better results, because combiningmultiple slices first may tend to average out noise and fine detail,which may contribute to the differences that are present in thetransformed data. Once the slices have been transformed, the resultingtransformed images may be combined to reduce noise and improverobustness.

The process of FIG. 2 may be repeated for a plurality of axial slicesrepresentative of a patient. The process of FIG. 2 may be repeated fordifferent data sets. The process of FIG. 2 may be repeated for any twoor more imaging data sets that are representative of the same anatomy,for example two or more imaging data sets that are representative of asingle axial slice.

The method of FIG. 2 has been described above for the simplest case oftwo imaging data sets. In some embodiments, the analysis circuitry 26may obtain from two imaging data sets only the central angle from thenon-overlapping data. However, knowledge of the central angle may besufficient for some motion compensation methods. In other embodiments,the analysis circuitry 26 may obtain further information from twoimaging data sets. For example, the analysis circuitry 26 may processthe difference data set to obtain an estimate of a range ofnon-overlapping angles.

In some embodiments, angular information is obtained by processing threeor more imaging data sets. For example, three or more imaging data setsmay be processed to obtain a complete range of rotation angles for eachof the three or more imaging data sets.

Consider the case in which three imaging data sets A, B, and C have beenreconstructed from CT scan data representative of a single axial slice.Each of the imaging data sets has been reconstructed from CT scan datafor a different range of gantry rotation angles. The offsets between theranges of gantry rotation angles are such that the ranges of A and Boverlap; the ranges of B and C overlap; and the ranges of A and Coverlap.

The computing apparatus 12 performs the process of FIG. 2 on each pairof imaging data sets, A-B, A-C and B-C. The computing apparatus 12determines a midpoint of a respective non-overlapping region for eachpair A-B, A-C, B-C. The determined midpoints, and the knowledge thateach imaging data set is reconstructed from a 180° range of data, may beused to obtain a complete range of rotation angles for all three imagingdata sets by simple algebra. Once the midpoints are known, there mayonly be one combination of angular ranges that would result in thosemidpoints.

In some motion compensation methods, imaging data sets are reconstructedthat have an offset of about 90°. For imaging data sets having an offsetof 90°, it may not be possible to use three imaging data sets A, B and Cto determine the full rotational ranges for three imaging data sets A,B, C by estimating for each pair A-B, A-C and B-C a midpoint of arespective non-overlapping region, since if A and B are 90° apart and Band C are 90° apart, A and C do not overlap.

In some embodiments, for example if there is no overlap between firstand third images A and C, difference data sets for overlapping pairs ofimages (for example, A-B, B-C) may be used to determine a range ofangles over which the Fourier transformations are significantlydifferent. For example, the analysis circuitry 26 may determine a rangeof angles for each of the bright regions 50, 52. In some embodiments,finding a range of non-overlapping angles may be less robust thanfinding a midpoint of the range of non-overlapping angles. However,within a given acquisition, it may be possible to compute relativeranges consistently.

In some circumstances, tolerances of the angular estimation may be below10° of angle. Lower tolerances may be used in some particular methods,for example in motion compensated reconstruction.

In some circumstances, additional information about the reconstructionmay be used in the determination of one or more gantry angles. Forexample, even if the computing apparatus 12 does not have informationabout the gantry angles for the data used in each individual imagingdata set, it may be known that consecutive imaging data sets arereconstructed from ranges that are 90° apart.

FIGS. 4a and 4b are schematic illustrations representing examples ofestimation of a midpoint of a non-overlapping range obtained from realdata. In the embodiment of FIGS. 4a and 4b , half-rotationreconstructions are spaced 90° apart.

Each of FIGS. 4a and 4b is representative of a sum of absolutedifferences of Fourier transformations over eight uniformly spacedslices, with some smoothing applied to the difference data set toimprove robustness.

In FIG. 4a , line 70 is representative of a 180° range of ground truthgantry angles for a first imaging data set. Line 72 is representative ofa 180° range of ground truth gantry angles for a second imaging dataset.

A difference data set was obtained from the first imaging data set andsecond imaging data set using the method described above with referenceto FIG. 2. A two-dimensional function 74 was fitted to the differencedata set. Line 76 shows the approximate principal angle of thedifference data set, determined from the fitting of the two-dimensionalfunction.

The approximate principal angle obtained using the method of FIG. 2 wasfound to be a good estimate of the midpoint of the non-overlapping rangeof gantry angles (which can be seen from the ground truth ranges 70,72).

In FIG. 4b , line 72 is representative of a range of a 180° ground truthgantry angles for a second imaging data set and line 78 isrepresentative of a 180° range of ground truth gantry angles for a thirdimaging data set. A difference data set was obtained from the secondimaging data set and third imaging data set using the method describedabove with reference to FIG. 2. A two-dimensional function 80 was fittedto the difference data set. Line 82 shows the approximate principalangle of the difference data set, determined from the fitting of thetwo-dimensional function.

Again, an approximate principal angle obtained using the method of FIG.2 was found to be a good estimate of the midpoint of the non-overlappingrange of gantry angles (which can be seen from the ground truth ranges72, 78).

The method of FIG. 2 may provide a method of determining angles ofgantry rotation automatically. For example, gantry rotation angles maybe determined from imaging data sets that are supplied from the CTscanner 14 without associated gantry rotation angles being supplied.Gantry rotation angles may be determined for stored imaging data sets.

Angles obtained using the process of FIG. 2 may be used in motionestimation and/or motion compensated reconstruction. In some methods ofmotion estimation, cardiac motion may be estimated based on a number ofreconstruction volumes (for example, three reconstruction volumes) thatare representative of very close time points. See, for example, U.S.patent application Ser. No. 14/519,564. In order to estimate motion, arelative time (corresponding to a relative angle) between reconstructionvolumes may be used. Different reconstruction volumes may be registeredto each other in order to determine motion occurring between thereconstruction volumes.

In some embodiments, angles obtained using the process of FIG. 2 may beused to determine a relative angle between imaging data sets, andtherefore to determine a relative time between imaging data sets. Thecomputing apparatus 12 may use the relative time or angle in a motionestimation process to estimate motion between imaging data sets.

In some embodiments, angles obtained using the process of FIG. 2 may beused in motion compensated reconstruction. The computing apparatus 12may create a new reconstruction of the data with reduced artifacts. Forexample, the computing apparatus 12 may register together a first andsecond imaging data sets corresponding to different scanning timeperiods. The computing apparatus 12 may use the registration todetermine a motion estimate, for example a warp field. The computingapparatus 12 may reconstruct a further imaging data set using theestimated motion, for example by using the method of Tang et al, Acombined local and global motion estimation and compensation method forcardiac CT, Proc. SPIE 9033, Medical Imaging 2014: Physics of MedicalImaging, 903304 (19 Mar. 2013).

For example the computing apparatus may divide an angular range of oneof the imaging data sets into a plurality of regions (in one example, 12regions of 15′ each), obtain partial reconstructions of each of theregions, interpolate the motion estimation to a time of each of theplurality of regions, transform the partial reconstructions toincorporate the interpolated motion estimation, and combine the partialreconstructions to obtain a new imaging data set in which motion hasbeen at least partially compensated.

In some embodiments, the computing apparatus 12 may perform motionestimation and/or motion compensated reconstruction without receivinggantry rotation angle information from the CT scanner 14, memory 20 ordata store.

In some existing systems, motion compensation methods may be tightlyintegrated into a CT product (for example, a CT scanner) to make use ofangular information available in the CT scanner.

A reconstruction stage of a motion compensation method may use knowledgeof angles of gantry rotation for images to be corrected. Some motionestimation methods may also use this information.

The method of FIG. 2 may allow motion compensation methods (or othermethods that use angular information) to be performed by a workstationthat does not have access to angular information available in thescanner 14. The method of FIG. 2 may be performed by a standaloneworkstation.

Gantry angle information may not normally be available to a workstationthat receives reconstructed data. By determining the angles of gantryrotation automatically from imaging data sets, motion estimation and/ormotion compensation methods that use such angular information may beapplied to imaging data sets.

Motion estimation and/or motion compensation methods may be applied topreviously-acquired data, for example data that has been stored in aPACS system. In some circumstances, motion estimation and/or motioncompensation methods may be applied to historic scan data which had beencaptured without contemplating its use in motion estimation and/ormotion compensation. In some circumstances, new motion estimation and/ormotion compensation techniques may be applied to data that was takenbefore the new motion estimation and/or motion compensation techniquesbecame available.

The system of FIG. 1 may be used to estimate angular parameters relatedto CT scan data. By estimating gantry rotation angles from imaging datasets, it may become possible to apply some motion compensation methodsto data where the angles are not otherwise recorded.

In further embodiments, angles obtained using the method of FIG. 2 maybe used in applications other than motion estimation and/or motionreconstruction. The angles may be used as input to any suitablealgorithm. For example, in some embodiments, angles estimated using themethod of FIG. 2 are used in a process of metal artifact reduction. Insome circumstances, artifacts in an image caused by a metal object (forexample, a dental filling, orthopedic plate, or spinal rod) may differin dependence on the angles of rotation of the data used to reconstructthe image. For example, X-rays may be scattered more when striking themetal object from a particular angle. In some embodiments, estimatingangles from imaging data sets may allow the imaging data set having thelowest level of metal artifacts to be selected. In some embodiment,estimated angles may be used to perform a method of removing or reducingmetal artifacts.

Embodiments describes above are embodiments in which a scanner gantryrotates around a patient or other subject. In other embodiments, asource and/or receiver may remain static while a patient or othersubject is rotated. In such embodiments, the method of FIG. 2 may beused to determine at least one angle of rotation of the patient. Ingeneral, the angles determined may be angles of relative rotation of atleast part of a scanner and at least part of a patient or other subject.

In the present embodiment, the scanner acquires CT data and reconstructsthat CT data to provide imaging data. In other embodiments, the scanneracquires data of any suitable modality (for example, CT, cone-beam CT,MR, PET, SPECT, X-ray or ultrasound) and uses a reconstruction methodsuitable for reconstructing imaging data sets from data of the acquiredmodality. The scanner may reconstruct data from the scanner to provideany appropriate two-dimensional or three-dimensional imaging data sets.In some embodiments, the scanner is a cone-beam CT scanner. In someembodiments, the imaging data sets are angiography imaging data sets.

The measurement volume may be any appropriate anatomical region of anyhuman or animal subject. The anatomical region may comprise any suitableanatomical structure, for example any organ (for example, heart, lung orliver) or vessel (for example, coronary artery). The anatomical regionmay be a region that is subject to motion (for example, heart motion).The anatomical region may be a region for which it is desired to performmotion estimation and/or motion compensation.

Certain embodiments provide a medical imaging method comprisingreceiving two or more 2D or 3D CT image datasets of a given portion of apatient, each dataset reconstructed from sinogram data over a givenperiod, such that the time periods of at least one pair of datasetsoverlap, and for at least one pair of image datasets, determining themidpoint and/or duration of the range of time periods for the firstdataset that do not overlap with the time period of the second dataset.

The determining of the midpoint and/or duration may comprise:

a) computing the 2D discrete Fourier transformation (DFT) of each imageof each of the pair of datasets;

b) computing the difference of the two DFTs computed in step a); and

c) determining the midpoint and/or size of the range of angles overwhich the difference computed in step b) has largest magnitude.

Step c) may comprise computing the sum of squares along many radiallines through the centre of the difference image, and returning theangle at which the sum of squares is largest.

Certain embodiments may provide a medical imaging method comprising:receiving three or more 2D or 3D CT image datasets of a given portion ofa patient, each dataset reconstructed from sinogram data over a giventime period, such that the time periods of at least one pair of datasetsoverlap; for at least two pairs of image datasets, determining the rangeof time periods for the first dataset that do not overlap with the timeperiod of the second dataset; and using the information from thedetermining of the range of time periods, determining the full range ofangles of CT gantry rotation for each of the datasets received.

Certain embodiments provide a method for correcting motion artifacts inCT image datasets, comprising: receiving three or more 3D CT imagedatasets of a given portion of a patient; estimating anatomical motionbetween at least two pairs of the datasets; determining the range ofangles of CT gantry rotation for each of the datasets; and using theestimated anatomical motion and determined range of angles inreconstructing a further CT image dataset with reduced motion artifacts.

Whilst particular circuitries have been described herein, in alternativeembodiments functionality of one or more of these circuitries can beprovided by a single processing resource or other component, orfunctionality provided by a single circuitry can be provided by two ormore processing resources or other components in combination. Referenceto a single circuitry encompasses multiple components providing thefunctionality of that circuitry, whether or not such components areremote from one another, and reference to multiple circuitriesencompasses a single component providing the functionality of thosecircuitries.

Whilst certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the invention. Indeed the novel methods and systems describedherein may be embodied in a variety of other forms; furthermore, variousomissions, substitutions and changes in the form of the methods andsystems described herein may be made without departing from the spiritof the invention. The accompanying claims and their equivalents areintended to cover such forms and modifications as would fall within thescope of the invention.

The invention claimed is:
 1. A medical imaging data processing apparatuscomprising: processing circuitry configured to: obtain a first imagingdata set comprising a set of pixels or voxels, the first imaging dataset being reconstructed from first measurement data representative ofmeasurements of a measurement volume obtained by relative rotation of amedical scanner and the measurement volume by a first range of anglesduring a first scanning time period; obtain a second imaging data setcomprising a set of pixels or voxels, the second imaging data set beingreconstructed from second measurement data representative ofmeasurements of the measurement volume obtained by relative rotation ofthe medical scanner and the measurement volume by a second range ofangles during a second scanning time period, wherein the second scanningtime period overlaps the first scanning time period such that someangles are included in both the first range of angles and the secondrange of angles; transform the first imaging data set to obtain a firsttransformed data set that is representative of the first measurementdata as a function of at least one of angle or time; transform thesecond imaging data set to obtain a second transformed data set that isrepresentative of the second measurement data as a function of at leastone of angle or time; and determine at least one angle of the firstrange of angles and/or second range of angles based on differencesbetween the first transformed data set and second transformed data setby comparing pixel values of the first transformed data set tocorresponding pixel values of the second transformed data set.
 2. Theapparatus according to claim 1, wherein the processing circuitrydetermines the at least one angle by: obtaining a difference data setrepresentative of the differences between the transformed first data setand transformed second data set; and obtaining the estimate of the atleast one angle based on the difference data set.
 3. The apparatusaccording to claim 2, wherein the processing circuitry obtains thedifference data set by subtracting the transformed first data set andtransformed second data set.
 4. The apparatus according to claim 1,wherein the processing circuitry transforms by applying to each of thefirst imaging data set and second imaging data set at least one of: aFourier transform, a discrete Fourier transform, a Fast Fouriertransform, a number-theoretic transform, a discrete weighted transform,a Chirp Z-transform.
 5. The apparatus according to claim 2, wherein theprocessing circuitry is further configured to apply a logarithm operatorto the difference data set.
 6. The apparatus according to claim 1,wherein the at least one angle comprises a midpoint and/or a boundary ofa non-overlapping range of angles that are included in one of the firstrange of angles and second range of angles but not in the other of thefirst range of angles and second range of angles.
 7. The apparatusaccording to claim 1, wherein the at least one angle comprises amidpoint and/or a boundary of an overlapping range of angles that areincluded in both the first range of angles and the second range ofangles.
 8. The apparatus according to claim 1, wherein the at least oneangle comprises at least one boundary of the first range of anglesand/or at least one boundary of the second range of angles.
 9. Theapparatus according to claim 2, wherein the processing circuitrydetermines the at least one angle based on a magnitude of elements ofthe difference data set.
 10. The apparatus according to claim 2, whereinthe processing circuitry determines the at least one angle of rotationby at least one of a) to e): a) determining a respective sum of squaresfor each of a plurality of radial lines through the difference data set;b) fitting a two-dimensional function to the difference data set; c)determining a profile along a circular trajectory around the centre ofthe difference data set; determining a profile along a circulartrajectory around the centre of the difference data set and obtaining aspectral decomposition of the profile; e) determining an angle of a lineof reflective symmetry of the difference data set.
 11. The apparatusaccording to claim 1, wherein the processing circuitry is furtherconfigured to obtain an estimate of motion between the first imagingdata set and second imaging data set using the determined at least oneangle.
 12. The apparatus according to claim 11, wherein the processingcircuitry is further configured to perform motion compensatedreconstruction using the estimate of motion.
 13. The apparatus accordingto claim 1, wherein the processing circuitry is further configured to:obtain a third imaging data set comprising a set of pixels or voxels,the third imaging data set being reconstructed from third measurementdata representative of measurements of the measurement volume obtainedby relative rotation of the medical scanner and the measurement volumeby a third range of angles during a third scanning time period, whereinthe third scanning time period overlaps each of the first and secondscanning time periods; transform the third imaging data set to obtain athird transformed data set that is representative of the thirdmeasurement data as a function of at least one of angle or time; andobtain an estimate of boundaries of the first range of angles, secondrange of angles and third range of angles based on the first transformeddata set, second transformed data set and third transformed data set.14. The apparatus according to claim 1, wherein the processing circuitrydetermines the at least one angle by estimating said at least one angle.15. The apparatus according to claim 1, wherein the measurement volumecomprises an anatomical region of a subject.
 16. The apparatus accordingto claim 15, wherein the anatomical region comprises at least one of avessel, a coronary artery, an organ, a heart, a lung, a liver.
 17. Theapparatus according to claim 14, wherein the measurement volumecomprises at least one metal object.
 18. The apparatus according toclaim 1, wherein the medical scanner comprises at least one of a CTscanner, a cone-beam CT scanner, an MRI scanner, a PET scanner, a SPECTscanner, an X-ray scanner, an ultrasound scanner.
 19. A medical imagingdata processing method comprising: obtaining a first imaging data setcomprising a set of pixels or voxels, the first imaging data set beingreconstructed from first measurement data representative of measurementsof a measurement volume obtained by relative rotation of a medicalscanner and the measurement volume by a first range of angles during afirst scanning time period; obtaining a second imaging data setcomprising a set of pixels or voxels, the second imaging data set beingreconstructed from second measurement data representative ofmeasurements of the measurement volume obtained by relative rotation ofthe medical scanner and the measurement volume by a second range ofangles during a second scanning time period, wherein the second scanningtime period overlaps the first scanning time period such that someangles are included in both the first range of angles and the secondrange of angles; transforming the first imaging data set to obtain afirst transformed data set that is representative of the firstmeasurement data as a function of at least one of angle or time;transforming the second imaging data set to obtain a second transformeddata set that is representative of the second measurement data as afunction of at least one of angle or time; and determining at least oneangle of the first range of angles and/or second range of angles basedon differences between the first transformed data set and secondtransformed data set by comparing pixel values of the first transformeddata set to corresponding pixel values of the second transformed dataset.
 20. A computer program product comprising a computer readablememory storing instructions that are executable to perform a method, themethod comprising: obtaining a first imaging data set comprising a setof pixels or voxels, the first imaging data set being reconstructed fromfirst measurement data representative of measurements of a measurementvolume obtained by relative rotation of a medical scanner and themeasurement volume by a first range of angles during a first scanningtime period; obtaining a second imaging data set comprising a set ofpixels or voxels, the second imaging data set being reconstructed fromsecond measurement data representative of measurements of themeasurement volume obtained by relative rotation of the medical scannerand the measurement volume by a second range of angles during a secondscanning time period, wherein the second scanning time period overlapsthe first scanning time period such that some angles are included inboth the first range of angles and the second range of angles;transforming the first imaging data set to obtain a first transformeddata set that is representative of the first measurement data as afunction of at least one of angle or time; transforming the secondimaging data set to obtain a second transformed data set that isrepresentative of the second measurement data as a function of at leastone of angle or time; and determining at least one angle of the firstrange of angles and/or second range of angles based on differencesbetween the first transformed data set and second transformed data setby comparing pixel values of the first transformed data set tocorresponding pixel values of the second transformed data set.